0.09/0.13	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.14	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.14/0.36	% Computer : n018.cluster.edu
0.14/0.36	% Model    : x86_64 x86_64
0.14/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory   : 8042.1875MB
0.14/0.36	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit : 1440
0.14/0.36	% WCLimit  : 180
0.14/0.36	% DateTime : Mon Jul  3 06:36:30 EDT 2023
0.14/0.36	% CPUTime  : 
66.01/8.65	% SZS status Unsatisfiable
66.01/8.65	
66.01/8.65	% SZS output start Proof
66.01/8.65	Axiom 1 (o_definition): apply(apply(o, X), Y) = apply(Y, apply(X, Y)).
66.01/8.65	Axiom 2 (q1_definition): apply(apply(apply(q1, X), Y), Z) = apply(X, apply(Z, Y)).
66.01/8.65	
66.01/8.65	Goal 1 (prove_fixed_point): apply(combinator, X) = X.
66.01/8.65	The goal is true when:
66.01/8.66	  X = apply(apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X), apply(apply(apply(q1, q1), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1)))), apply(o, apply(q1, q1))))
66.01/8.66	
66.01/8.66	Proof:
66.01/8.66	  apply(combinator, apply(apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X), apply(apply(apply(q1, q1), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1)))), apply(o, apply(q1, q1)))))
66.01/8.66	= { by axiom 2 (q1_definition) R->L }
66.01/8.66	  apply(apply(apply(q1, combinator), apply(apply(apply(q1, q1), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1)))), apply(o, apply(q1, q1)))), apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X))
66.01/8.66	= { by axiom 2 (q1_definition) R->L }
66.01/8.66	  apply(apply(apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))), apply(apply(q1, q1), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X))
66.01/8.66	= { by axiom 1 (o_definition) R->L }
66.01/8.66	  apply(apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1)))), apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X))
66.01/8.66	= { by axiom 2 (q1_definition) R->L }
66.01/8.66	  apply(apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X), apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))))
66.01/8.66	= { by axiom 2 (q1_definition) R->L }
66.01/8.66	  apply(apply(apply(q1, apply(apply(o, apply(q1, q1)), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1))))), X), apply(apply(apply(q1, q1), apply(apply(q1, apply(q1, combinator)), apply(o, apply(q1, q1)))), apply(o, apply(q1, q1))))
66.01/8.66	% SZS output end Proof
66.01/8.66	
66.01/8.66	RESULT: Unsatisfiable (the axioms are contradictory).
66.01/8.67	EOF